Relativistic Radiative Transitions

We have calculated the summed oscillator strength for a $K$ electron in the Coulomb field of a lead nucleus, using calculations of the oscillator strength for discrete transitions, and the oscillator density for absorption to the continuum. We obtain 86% of the value unity given by the nonrelativistic Thomas-Reiche-Kuhn sum rule. We also use dispersion theory to calculate the forward scattering amplitude as a function of photon energy. Our numerical values for the forward scattering amplitude are in good agreement with Brown's values for a $K$ electron of mercury at 1.7, 3.4, and 6.8 times the binding energy. We also compare with our calculations of the forward scattering amplitude by a nonrelativistic electron in a Coulomb field.